Propagation of compression waves in elastic rods of variable cross section

1977 ◽  
Vol 13 (11) ◽  
pp. 1149-1156
Author(s):  
I. G. Filippov
Keyword(s):  
Cross Section ◽  
Variable Cross Section ◽  
Elastic Rods ◽  
Variable Cross ◽  
Compression Waves

On the theory of rods II. Developments by direct approach

1974 ◽  
Vol 337 (1611) ◽  
pp. 485-507 ◽  
Keyword(s):  
Cross Section ◽  
Variable Cross Section ◽  
Direct Approach ◽  
Elastic Rods ◽  
Variable Cross ◽  
Uniform Cross Section ◽  
Axes Of Symmetry

This paper, which may be regarded as a companion to part I under the same title, is concerned with some aspects of both the nonlinear and the linear theories of elastic rods by a direct approach based on the theory of a Cosserat curve with two directors. Special attention is given to the development of the linear isothermal theory of straight isotropic rods of variable cross-section possessing two axes of symmetry. The resulting equations, which are applicable to rods of non-uniform section, separate into those appropriate for extensional, torsional and flexural modes of deformation. Application of these results to torsion and flexure of non-uniform rods are considered, and the problem of identification of constitutive coefficients for rods of uniform cross-section is dealt with at some length.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

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